let s be State of SCM+FSA ; :: thesis: for Ig being good Program of SCM+FSA
for j being parahalting Instruction of SCM+FSA st ( Ig is parahalting or ( Ig is_halting_on Initialize s & Ig is_closed_on Initialize s ) ) holds
DataPart (IExec (Ig ';' j),s) = DataPart (Exec j,(IExec Ig,s))
let Ig be good Program of SCM+FSA ; :: thesis: for j being parahalting Instruction of SCM+FSA st ( Ig is parahalting or ( Ig is_halting_on Initialize s & Ig is_closed_on Initialize s ) ) holds
DataPart (IExec (Ig ';' j),s) = DataPart (Exec j,(IExec Ig,s))
let j be parahalting Instruction of SCM+FSA ; :: thesis: ( ( Ig is parahalting or ( Ig is_halting_on Initialize s & Ig is_closed_on Initialize s ) ) implies DataPart (IExec (Ig ';' j),s) = DataPart (Exec j,(IExec Ig,s)) )
set I = Ig;
assume A1: ( Ig is parahalting or ( Ig is_halting_on Initialize s & Ig is_closed_on Initialize s ) ) ; :: thesis: DataPart (IExec (Ig ';' j),s) = DataPart (Exec j,(IExec Ig,s))
then A2: for a being Int-Location holds (IExec (Ig ';' j),s) . a = (Exec j,(IExec Ig,s)) . a by Th12;
for f being FinSeq-Location holds (IExec (Ig ';' j),s) . f = (Exec j,(IExec Ig,s)) . f by A1, Th13;
hence DataPart (IExec (Ig ';' j),s) = DataPart (Exec j,(IExec Ig,s)) by A2, SCMFSA6A:38; :: thesis: verum